Hard disks for computers must spin evenly, and one departure from level is called roll. Probability and Statistics

Question

Hard disks for computers must spin evenly, and one departure from level is called roll. The roll for any disk can be modeled as a normal random variable with mean 0.1240 mm. 16 random sample disks were collected, and the sample variance is 0.001014. What's the probability that the sample mean will lie between 0.1032 mm and 0.1380 mm?

Answer 1

It would be helpful if you tell how you are solving these problems in your class - statistical calculator, computer software, or tables. I would also like to see what work you have done on this problem. First, you need to figure out the mean and standard error for a normal distribution. They tell you the mean in the problem. Next, find the standard deviation by taking the square root of the variance. Then, the standard error for sets of 16 disks is the standard deviation divided by the square root of 16. See if you get

SE = 0.00796. I use a TI-83 or 84 to do these problems. You could press the Distr key (above the VARS key). Then select nornmalcdf and enter the mean, standard error, and the two endpoints of the interval in the problem (0.1032 and 0.1380). If you submit your work and your final answer, someone here can check it for you. If you are not using a statistical calculator, please submit the question and your work and tell what method you use in class to do the computations.